Low frequency piezoelectric crystal



27, 1940' J. M. WOLFSKILL 2,213,931

LOW FREQUENCY PIEZOELECTRIC CRYSTAL Filed April 8, 1938 2 Sheets-Sheet 1 IT. 2. 5a IL E 5 1) INVEN TOR.

Patented Aug. 27, 1940 UNITED STATES PATENT OFFICE LOW FREQUENCY PIEZOELECTRIG CRYSTAL man Application April 8, 1988, Serial No. 200,980

2 Claims This invention relates to piezoelectric devices, in general and more particularly to an improved type of low frequency quartz crystal.

An object of my invention is to provide a crystal having a low frequency-temperature coefficient, and having a substantially single frequency response.

Another object is to reduce the cost of low temperature coefiicient crystals in the range from 50 kc. to 500 kc., by a system, or method of cutting and grinding.

Another object is to set forth a method of grinding such that the temperature coemcient of the crystal may be made either zero, positive, or negative, over wide ranges of temperature, simply by grinding and proportioning the dimensions of the crystal accordingly.

Another object is to provide a crystal in which the angle at which the crystal is cut with respect to the crystallographic axis, may vary over rather wide limits, and yet the temperature coefiicient can be controlled by a simple manipulation of the dimensional ratios.

Still another feature of the invention is to produce a crystal having a high length-frequency coeflicient, such that sizable crystals can be produced in length-breadth oscillators or bar type oscillators up to 500 kc.

I-leretofore, when low temperature coefilcient crystals were to be made in the range from 200 kc. to 500 kc., a thickness vibration, generally a shear vibration, was employed, and the frequency controlling dimension (thickness of the crystal) was an appreciable part of the length and breadth of the crystal. There was, therefore, a tendency for the crystal to oscillate at several frequencies, and to jump from one frequency to another as the temperature was varied, or as circuit conditions changed. It is extremely difficult to obtain a crystal of this type which has a zero temperature coeflicient over a wide temperature range, and which will not jump irequency.

By using crystals of my invention, the frequency drift with temperature is controllable after the crystal has been cut at the specified angle. This angle is not critical, and even if a slight error is made in the cutting, it may be compensated for by changing the dimensional ratio slightly. The invention will be more fully understood from the following description taken with the drawings in which, briefly, Fig. la is a view showing a piezoelectric crystal element cut from a raw quartz crystal, this view illustrates the position of the plate in the quartz hexahedronal crystal with respect to the X or electric axis, and the Y or mechanical axis; Fig. 1b shows the angle at which the crystal plate is cut with respect to the Z or optic axis; Fig. 2 is a perspective view showing the crystal plate with respect to the various crystallographic axes; Fig. 3a shows the crystal element with the important dimensions; Fig. 3b is another view showing the crystal element; Figs. 4 and 5 are graphs showing characteristics of crystal plates cut in accordance with this invention.

Referring to Figs. 1a, 1b and 2 in detail reference numeral 2 designates the crystal plate cut from the native quartz crystal. The plate 2 is cut from the crystal in the manner shown, with the principal surfaces 3 and 4 cut at an angle a with respect to the optic or Z axis. The principal surfaces 3 and 4 are cut substantially parallel to the electric or X axis.

The values of the angle 0 may vary i3 from the specified value. However, for best operation and control of the temperature drift, I have found that the plates should be cut at angles of +42 and 55. These angles refer to righhanded quartz. Figs. 3a and 312 show the actual crystal, as cut from the raw quartz, the shorter dimension of the rectangle "being the electflc axis, and the longer dimension the new optical or Z prime axis.

By grinding the crystal in Fig. 3a to the dotted lines 2a, the dimensional ratio m of width W to length L is increased. It is this ratio which is resignated as m, which controls the drift of the crystals. By grinding the crystal in Fig. 3b to the dotted lines 22) shown, the dimensional ratio m is decreased. Fig. 4; shows a plurality of curves (1 to g inclusive illustrating how the frequency drift of a 300 kilocycle crystal varies over a wide temperature range as the dimensional ratio m is varied. By frequency drift is meant the cycles change in frequency for a given frequency crystal. The curves illustrated in Fig. 4 are for a 800 kilocycle crystal and show the actual cycles change with temperature rather than a percentage change. However another ordinate is included in Fig. 4, designated as Frequency change in cycles 1000 kc. base frequency from which the frequency temperature coefiicient of the crystal may be easily obtained. This ordinate was obtained by multiplying the values of the Frequency change in cycles ordinate by a factor of 3 since the curves were plotted using a 300 kilocycle crystal and conventionally the frequency temperature coeficient is based upon cycles change per million per degree. Zero ire-=- iii quency drift can be obtained over any specified temperature range, or a specified drift over the complete range may be obtained simply by choosing the proper dimensional ratio from the curves. These curves, shown by way of example only, are for the +42 crystal, and apply for anyfrequency between 150 kc. to 500 kc. The general shapes of these curves for the various values of 112, however,.apply to any crystal. After establishing the proper ratio, all that has to be done in grinding a crystal to a particular frequency is to maintain this ratio by grinding on both the length L and the width W. I

The +42 bar has a frequency length coefiicient of approximately 2.2 x 10 giving a crystal at 200 kc., approximately 1.1" long x .6" wide x .090" thick. The thickness has relatively little effect on the drift or frequency, and does not appreciably change the frequency temperature curves for various ratios. For the lower frequency crystals, 50 kc. to 150 kc., the 55" cut bar is used. This has a relatively low frequencylength coefiicient, being approximately 1.1 x when the length is expressed in inches. This may be expressed as follows:

Length coefllcient A representative crystal for 100 kc. would be 1.1" long x .65 wide x .090" thick.

Curves showing the variation of frequency change with temperature for various width to length ratios m of the 55 cut crystal are shown in Fig. 5. For this crystal, the drift decreases with decreasing dimensionalratio, becoming zero, and increasing in the negative direction as a dimensional ratio of .60 is passed, .60 being the optimum ratio of width to length for a zero frequency drift over the temperature range from zero to 60 C. For the +42 cut bar, the frequency drift decreases with increasing dimensional ratio, passing through zero at a ratio of .535, and increasing in the negative direction as this point is passed.

The curves illustrated in Figs. 4 and 5 may be referred to as two families of curves, the curves of Fig. 4 consisting of one family pertaining to the +42 degree bar type crystal and those of Fig. 5 consisting of another family pertaining to the 55 degree bar type crystal. In the case of Fig. 4 a crystal ground to 300 kilocycles at 30 degrees centigrade was used consequently all of the curves, that is, curves a, b, c, d, e, f and 9 pass through the zero at 30 degrees, the zero corresponding in this case to the crystal frequency of 300 kilocycles. As the temperature departs from 30 degrees upward-the crystal having the ratio of m equal to 0.51 increases in frequency as illustrated by the curve 9 until its frequency is 300,020 cycles at 60 degrees. 'On the other hand in a crystal having the ratio m equal to 0.57, an increase in temperature to 60 degrees will reduce its frequency by approximately 30 cycles from the 300,000 cycles. By following the curve 12 corresponding to m ratio of 0.54 a crystal of almost constant frequency over the temperature range given, is obtained.

The curves of Fig. 5 are similar to those of Fig. 4 in that they also give the frequency change with temperature for crystals having different m ratios.

It is obvious that if the curves were plotted using crystals ground to frequency at temperatures other than 30 degrees centigrade that the curves would intersect at this other temperature,

However their general shape or shapes would be like that illustrated.

In Fig. 4 an additional ordinate has been provided for converting the actual cycles change for the 300 kilocycle crystal to cycles change for a 1000 kilocycle crystal to obtain the cycles change per million. By dividing the total frequency change obtained from this'ordinate by the temperature range over which this total frequency change is obtained, the frequency temperature coemcient for each of the m ratios may be obtained. A similar ordinate may be provided to Fig. 5 simply by multiplying the fllustrated values by 10 since a 100 kilocycle crystal was used in obtaining the curves.

The type of vibration employed in both these crystals is a combination shear and longitudinal; that is, the frequency is controlled by both the length and the width. However, what is meant here is that the length is the main frequency determining dimension, but the width also affects the frequency and it is for this reason that the ratios must be held within certain limits. If the m values are held tothe limits shown on the curves, the formulas for determining the frequency from the length will hold. For example, a 100 kc. crystal of the minus 55 cut, would be 1.1" long according to the formula, and as long as the ratio was between .55 and .65, the constant will remain approximately the same. It is felt that the dimensions of the crystal are suficiently defined from the ratio curves and the length frequency formula. The main features of these bars are that the frequency drift may be readily controlled after the crystal has been cut; that is, extreme precision in cutting at the required angle is not necessary; also, any predetermined frequency drift may be obtained, or any shape of the frequency temperature curve may be obtained.

A novel feature of the +42 bar is that for a length oscillator, the crystal is extremely large for a given frequency, the frequency length cceificient being twice that for any fundamental bar type oscillator previously known to the art.

From the foregoing specification it will be ob- I served that I have described this invention in detail with respect to certain embodiments thereof. I do not, however, desire to limit this invention to the exact details shown and described except insofar as those details may be defined by the claims.

I claim:

1. A method of producing a bar type low frequency piezoelectric crystal element adapted to vibrate in the combination shear and longitudinal modes, said crystal element being characterized in that the frequency drift caused by temperature variation may be readily controlled after the crystal element has been cut from the native crystal, comprising the steps of: cutting a crystal element from the native crystal with the major faces of said crystal element disposed at an angle of approximately +42 degrees with respect to the optic axis and substantially parallel to the electric axis, determining the frequencydrift-with-temperature change of said crystal element for different ratios of width W to length L dimensions of said crystal element, selecting the frequency temperature coeffic'ient desired for said crystal element, grinding the width W and length L dimensions of said crystal element so that the ratio W L is between 0.51 and 0.57 depending upon the frequency temperature coeificient desired and selected, and grinding both of the dimensions W and L maintaining the aforesaid selected ratio therebetween until the desired frequency is obtained.

2. A method of producing a bar type low frequency piezoelectric crystal element adapted to vibrate in the combination shear and longitudinal modes, said crystal element being characterized in that the frequency drift caused by temperature variation may be readily controlled after the crystal element has been cut from the native crystal, comprising the steps. of: cutting a crystal element from the native crystal with the major faces of said crystal element disposed at an angle of approximately 55 degrees with respect to the optic axis and substantially par allel to the electric axis, determining the frequency-drift-with-temperature change of said crystal element for different ratios of width W to length L dimensions of said crystal element, seiecting'the frequency temperature coefiicient desired for said crystal element, grinding the Width W and length L dimensions of said crystal element so that the ratio is between 0.55 and 0.85 depending upon the frequency temperature coefiicient desired and selected, and grinding both of the dimensions W and L maintaining the aforesaid selected ratio therebetween until the desired frequency is obtained.

JOHN M. WOLFSKILL. 

